{"paper":{"title":"Rademacher functions in Morrey spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Lech Maligranda, Sergei V. Astashkin","submitted_at":"2015-06-23T05:07:53Z","abstract_excerpt":"The Rademacher functions are investigated in the Morrey spaces M(p,w) on [0,1] for 1 \\le p <\\infty and weight w being a quasi-concave function. They span l_2 space in M(p,w) if and only if the weight w is smaller than the function log_2^{-1/2}(2/t) on (0,1). Moreover, if 1 < p < \\infty the Rademacher sunspace R_p is complemented in M(p,w) if and only if it is isomorphic to l_2. However, the Rademacher subspace is not complemented in M(1,w) for any quasi-concave weight w. In the last part of the paper geometric structure of Rademacher subspaces in Morrey spaces M(p,w) is described. It turns out"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.06862","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}